A squeaky door knob can be absolutely maddening if it isn't quickly remedied. The best way to fix a squeaky door knob is usually the simplest and most obvious: lubricate it. WD-40 or other penetrating oils are the perfect tool for this because they come in cans designed to direct a fine stream of oil directly into the offending part of the door knob mechanism.
Wiggle the plate where the door knob meets the door to see if it's loose. If it is, use a screwdriver to tighten the screws until the knob plate sits evenly against the surface of the door.
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Turn the door knob from both sides of the door to determine whether it still squeaks and, if so, on which side (it may be one or both).
Apply a thin stream of WD-40 or another penetrating oil to the seam where the actual knob you grip to open the door turns inside a plate mounted to the door. The ideal tool for this is a penetrating oil can with a thin straw nozzle attached to direct the flow of oil.
Turn the door knob back and forth rapidly to distribute the WD-40 inside the mechanism. If the knob still squeaks, apply the WD-40 around the opening where the bolt or half-bolt protrudes from the door's edge. Work the knob back and forth again to distribute the oil, then let it sit for about five minutes.
Check for the squeak again and apply more WD-40 as necessary.